For the gas temperature, the user can specify either a fixed temperature value, or request solution of an energy balance in the reactor. The energy balance is determined by considering a control volume that includes the reactor, the reactor walls, and any deposited material therein. The following equation for the total internal energy of the reactor system is then

(8–22)

The total internal energy consists of the internal energy of the gas, surface phases, deposited or etched solid phases, and walls. is the net heat flux directed out of the reactor. can either be specified directly as a constant ( QLOS keyword) or can be specified in terms of a constant heat transfer coefficient, ( HTRN keyword), and ambient temperature, , as follows:

(8–23)

refers to energy deposited into the gas in the reactor. The term represents the work done by the control volume on the external world. For plasma systems, this can represent the power deposited through Joule heating into the plasma by acceleration of charged species along electric fields. This term will be discussed in more detail in the description of the electron energy equation below.

The time derivative of the internal energy can be equated with the time derivative of the enthalpy, minus the time rate of change of the product of pressure and volume:

(8–24)

(8–25)

The left-hand side of Equation 8–22 then becomes:

(8–26)

We neglect the term on the right-hand-side that represents the heat capacity contribution from the walls. Expansion of the gas-phase contribution in Equation 8–26 yields a heat balance for each reactor module:

(8–27)

where is the specific enthalpy of the gas mixture equal to the sum of the product of the species mass fraction and the pure species specific enthalpy. Note that in a multi-temperature system, the species enthalpies are evaluated at the species temperature , which may differ from the mean gas temperature. In thermal systems, all equal , the gas temperature. represents the species specific heat capacity at constant pressure. Expansion of the bulk and surface contributions to Equation 8–26 yields:

(8–28)

If we neglect the time dependence of the bulk- and surface-phase species enthalpies and molecular weights, and make use of Equation 8–11 , Equation 8–28 is greatly simplified to:

(8–29)

Combining Equation 8–1 , Equation 8–2 , Equation 8–22 , Equation 8–26 , Equation 8–27 , and Equation 8–29 gives the transient energy equation for solving the gas temperature, as follows:

(8–30)

Here we define as the mean gas specific heat excluding the contribution of the electrons, since we assume that the electron temperature may be significantly different from the gas temperature. All other species are assumed to be in thermal equilibrium at the gas temperature . In other words,

(8–31)

where the subscript, , indicates the electron species. When no electrons are present Equation 8–30 reverts back to the thermal-equilibrium case and the mean specific heat is merely the mass-averaged value of all species components. The actual form of the gas energy equation solved is the result of subtracting the electron energy equation from Equation 8–30 . This form is presented after the introduction of the electron energy equation in the following section.

Heat release rates from gas-phase and/or surface reactions are calculated from the instantaneous chemical state of the reactor. In many cases, the time history of the heat release rate can be very noisy because of the underlying chemical system or the lack of time resolution during integration. The fluctuations in the heat release rate profile make accurate calculation of the total heat release from chemical reactions extremely challenging. In cases where precise time-profiles of heat release from gas-phase and/or surface reactions are needed, optional heat release equations can be included in the calculation. These heat release equations, one for gas-phase reactions and the other for surface reactions, are only used to provide smoother and more accurate time profiles of heat releases; they are "placeholder" equations and should not affect the other equations. The equations used to obtain the accumulated heat release from gas-phase and surface reactions are given respectively in Equation (a) and (b) as:

(8–32)

(8–33)